Extensions of locally compact abelian, torsion-free groups by compact torsion abelian groups

Let $X$ be a compact torsion abelian group. In this paper, we show that an extension of $F_p$ by $X$ splits where $F_p$ is the p-adic number group and $p$ a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by $X$ is not split.